The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
08 Mar 1998-Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences (The Royal Society)-Vol. 454, Iss: 1971, pp 903-995
TL;DR: In this paper, a new method for analysing nonlinear and nonstationary data has been developed, which is the key part of the method is the empirical mode decomposition method with which any complicated data set can be decoded.
Abstract: A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the empirical mode decomposition method with which any complicated data set can be dec...
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TL;DR: A taxonomy is proposed and outline the four families in time series data augmentation, including transformation-based methods, pattern mixing, generative models, and decomposition methods, and their application to time series classification with neural networks.
Abstract: In recent times, deep artificial neural networks have achieved many successes in pattern recognition. Part of this success can be attributed to the reliance on big data to increase generalization. However, in the field of time series recognition, many datasets are often very small. One method of addressing this problem is through the use of data augmentation. In this paper, we survey data augmentation techniques for time series and their application to time series classification with neural networks. We propose a taxonomy and outline the four families in time series data augmentation, including transformation-based methods, pattern mixing, generative models, and decomposition methods. Furthermore, we empirically evaluate 12 time series data augmentation methods on 128 time series classification datasets with six different types of neural networks. Through the results, we are able to analyze the characteristics, advantages and disadvantages, and recommendations of each data augmentation method. This survey aims to help in the selection of time series data augmentation for neural network applications.
198 citations
Cites methods from "The empirical mode decomposition an..."
...Takahashi et al. [74] proposed a method called Equalized Mixture Data Augmentation (EMDA), which mixes two sounds of the same class with randomly selected timings....
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...In addition to mixing sounds, EMDA perturbs the sound by boosting or attenuating particular frequency bands....
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...Due to the nature of using the frequency domain, data augmentations in this area are generally used for sound recognition, e.g. EMDA has been used for acoustic event detection [74] and animal audio classification [75] and SFM has been used for speech [56]....
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...Empirical Mode Decomposition (EMD) [102] is a method of decomposing nonlinear and non-stationary signals and it has shown to improve classification by using it as a decomposition method for data augmentation of noisy automobile sensor data in a CNN-LSTM [103]....
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TL;DR: A comprehensive literature review on the applications of digital signal processing, artificial intelligence and optimization techniques in the classification of PQ disturbances and a comparison of various classification systems is presented in tabular form.
Abstract: The increasing trend towards renewable energy sources requires higher power quality (PQ) at the generation, transmission and distribution systems. The PQ disturbances are produced due to the nonlinear loads, power electronic converters, system faults and switching events. The utilities and consumers of electric power are expected to acquire ideal voltage and current waveforms at rated power frequency. The development of new techniques for the automatic classification of PQ events is at present a major concern. This paper presents a comprehensive literature review on the applications of digital signal processing, artificial intelligence and optimization techniques in the classification of PQ disturbances. Various signal processing techniques used for the feature extraction such as Fourier transform, wavelet transform, S-transform, Hilbert transform, Gabor transform and their hybrids have been reviewed. The artificial intelligent techniques used for the pattern recognition such as artificial neural network, fuzzy logic, support vector machine are reviewed in detail. The optimization techniques used for the optimal feature selection such as genetic algorithm, particle swarm optimization and ant colony optimization are also reviewed. A comparison of various classification systems is presented in tabular form which highlights the important techniques used in the field of PQ disturbance monitoring. The comparison of research works carried out on the classification of PQ disturbances points out that many researchers have focussed on the feature extraction and classification techniques. Only few authors have used the feature selection techniques for selecting the best suitable features. This review may be considered a valuable source for researchers as a reference point to explore the opportunities for further improvement in the field of PQ classification.
196 citations
TL;DR: A computer-aided detection system to aid in the detection of F EEG signals has been developed, and the performance of nonlinear features for differentiating F and NF EEG signals is compared.
195 citations
Cites methods from "The empirical mode decomposition an..."
...[10] A.B. Das, M.I.H. Bhuiyan, Discrimination and classification of focal and nonfocal EEG signals using entropy-based features in the EMD-DWT domain, Biomed....
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...These decomposition approaches include the EMD [51], DWT [52], DT-CWT [53], WFB [54], TQWT [55], FAWT [56], and EWT [57]....
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...Sharma et al. [6] decomposed EEG signals with an empirical mode decomposition (EMD) technique and extracted entropy features....
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...Das et al. [10] combined two decomposition methods, namely the EMD and DWT, and applied these methods to the data....
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...tion approaches include the EMD [51], DWT [52], DT-CWT [53],...
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TL;DR: In this article, a fault diagnosis method based on local mean decomposition (LMD) and extreme learning machine (ELM) is proposed for rolling bearings under variable conditions. But, it is difficult to diagnose and identify different fault types of rolling bearings.
194 citations
TL;DR: Recent advances initially made in the study of ocean waves are applied to study the blood pressure waves in the lung to show that a signal can be described by a sum of a series of intrinsic mode functions, each of which has zero local mean at all times.
Abstract: Almost all variables in biology are nonstationarily stochastic. For these variables, the conventional tools leave us a feeling that some valuable information is thrown away and that a complex phenomenon is presented imprecisely. Here, we apply recent advances initially made in the study of ocean waves to study the blood pressure waves in the lung. We note first that, in a long wave train, the handling of the local mean is of predominant importance. It is shown that a signal can be described by a sum of a series of intrinsic mode functions, each of which has zero local mean at all times. The process of deriving this series is called the “empirical mode decomposition method.” Conventionally, Fourier analysis represents the data by sine and cosine functions, but no instantaneous frequency can be defined. In the new way, the data are represented by intrinsic mode functions, to which Hilbert transform can be used. Titchmarsh [Titchmarsh, E. C. (1948) Introduction to the Theory of Fourier Integrals (Oxford Univ. Press, Oxford)] has shown that a signal and i times its Hilbert transform together define a complex variable. From that complex variable, the instantaneous frequency, instantaneous amplitude, Hilbert spectrum, and marginal Hilbert spectrum have been defined. In addition, the Gumbel extreme-value statistics are applied. We present all of these features of the blood pressure records here for the reader to see how they look. In the future, we have to learn how these features change with disease or interventions.
194 citations
References
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TL;DR: In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.
Abstract: Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with trajectories in phase space For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states. Systems with bounded solutions are shown to possess bounded numerical solutions.
16,554 citations
"The empirical mode decomposition an..." refers background in this paper
...(ii) Lorenz equation The famous Lorenz equation (Lorenz 1963) was proposed initially to study deterministic non-periodic flow....
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01 Jan 1974
TL;DR: In this paper, a general overview of the nonlinear theory of water wave dynamics is presented, including the Wave Equation, the Wave Hierarchies, and the Variational Method of Wave Dispersion.
Abstract: Introduction and General Outline. HYPERBOLIC WAVES. Waves and First Order Equations. Specific Problems. Burger's Equation. Hyperbolic Systems. Gas Dynamics. The Wave Equation. Shock Dynamics. The Propagation of Weak Shocks. Wave Hierarchies. DISPERSIVE WAVES. Linear Dispersive Waves. Wave Patterns. Water Waves. Nonlinear Dispersion and the Variational Method. Group Velocities, Instability, and Higher Order Dispersion. Applications of the Nonlinear Theory. Exact Solutions: Interacting Solitary Waves. References. Index.
8,808 citations
Book•
01 Jan 1971
TL;DR: A revised and expanded edition of this classic reference/text, covering the latest techniques for the analysis and measurement of stationary and nonstationary random data passing through physical systems, is presented in this article.
Abstract: From the Publisher:
A revised and expanded edition of this classic reference/text, covering the latest techniques for the analysis and measurement of stationary and nonstationary random data passing through physical systems. With more than 100,000 copies in print and six foreign translations, the first edition standardized the methodology in this field. This new edition covers all new procedures developed since 1971 and extends the application of random data analysis to aerospace and automotive research; digital data analysis; dynamic test programs; fluid turbulence analysis; industrial noise control; oceanographic data analysis; system identification problems; and many other fields. Includes new formulas for statistical error analysis of desired estimates, new examples and problem sets.
6,693 citations
"The empirical mode decomposition an..." refers background in this paper
...A brief tutorial on the Hilbert transform with the emphasis on its physical interpretation can be found in Bendat & Piersol (1986)....
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01 Jan 1946
5,910 citations
"The empirical mode decomposition an..." refers methods in this paper
...In order to obtain meaningful instantaneous frequency, restrictive conditions have to be imposed on the data as discussed by Gabor (1946), Bedrosian (1963) and, more recently, Boashash (1992): for any function to have a meaningful instantaneous frequency, the real part of its Fourier transform has…...
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TL;DR: In this paper, the authors used the representations of the noise currents given in Section 2.8 to derive some statistical properties of I(t) and its zeros and maxima.
Abstract: In this section we use the representations of the noise currents given in section 2.8 to derive some statistical properties of I(t). The first six sections are concerned with the probability distribution of I(t) and of its zeros and maxima. Sections 3.7 and 3.8 are concerned with the statistical properties of the envelope of I(t). Fluctuations of integrals involving I2(t) are discussed in section 3.9. The probability distribution of a sine wave plus a noise current is given in 3.10 and in 3.11 an alternative method of deriving the results of Part III is mentioned. Prof. Uhlenbeck has pointed out that much of the material in this Part is closely connected with the theory of Markoff processes. Also S. Chandrasekhar has written a review of a class of physical problems which is related, in a general way, to the present subject.22
5,806 citations
"The empirical mode decomposition an..." refers background in this paper
...In general, if more quantitative results are desired, the original skeleton presentation is better; if more qualitative results are desired, the smoothed presentation is better....
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...Therefore, the parameter, ν, defined as N21 −N20 = 1 π2 m4m0 −m22 m2m0 = 1 π2 ν2, (3.7) offers a standard bandwidth measure (see, for example, Rice 1944a, b, 1945a, b; Longuet-Higgins 1957)....
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